Solve the equation.
-$$\left| 9 x ^ { 3 } + 3 x ^ { 2 } - 6 x \right| = 0$$
A) $\left\{ \frac { 3 } { 2 } , 1,0 \right\}$

B) $\left\{ \frac { 3 } { 2 } , 0 \right\}$

C) $\left\{ \frac { 2 } { 3 } , - 1,0 \right\}$

D) $\left\{ \frac { 3 } { 2 } , - 1 \right\}$

Question

Solve the equation.
-$$\left| 9 x ^ { 3 } + 3 x ^ { 2 } - 6 x \right| = 0$$
A) $\left\{ \frac { 3 } { 2 } , 1,0 \right\}$

B) $\left\{ \frac { 3 } { 2 } , 0 \right\}$

C) $\left\{ \frac { 2 } { 3 } , - 1,0 \right\}$

D) $\left\{ \frac { 3 } { 2 } , - 1 \right\}$

Quizplus · Accepted Answer

The equation inside the absolute value is $9x^3 + 3x^2 - 6x = 0$. Factoring gives $3x(3x^2 + x - 2) = 0$. Solving $3x = 0$ gives $x = 0$. Solving $3x^2 + x - 2 = 0$ using the quadratic formula gives $x = \frac{2}{3}$ and $x = -1$. Thus, the solution set is $\left\{ \frac{2}{3}, -1, 0 \right\}$.

Solve the Equation ∣9x3+3x2−6x∣=0\left| 9 x ^ { 3 } + 3 x ^ { 2 } - 6 x \right| = 0​9x3+3x2−6x​=0

Solve the Equation $\left| 9 x ^ { 3 } + 3 x ^ { 2 } - 6 x \right| = 0$